England, who came into cricket's second 50-over tournament having lost a home one-day series to New Zealand, scored 179 for three to knock off the required runs in 37.3 overs and win by seven wickets with Jonathan Trott notching 82 not out.
David Miller top scored for pre-tournament favourites South Africa with 56 not out as the Proteas lasted only 38.4 overs.
The second semi-final between world champions India and Sri Lanka takes place on Thursday in Cardiff with England awaiting the winners at Edgbaston in Birmingham on Sunday.
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